Fitted mesh numerical method for two-parameter singularly perturbed partial differential equations with large time lag

Abstract

In this study, we devise a parameter-uniform second-order numerical method for two-parameter singularly perturbed partial differential equations with large time lag. The equations are discretized using the Crank–Nicolson method in time direction on uniform mesh and the cubic spline method in space direction on a Bakhvalov mesh. The theoretical parameter-uniform convergence analysis and the numerical results proves that the present method gives second-order $\varepsilon -$uniform convergence both in space and time directions. Two numerical experiments are performed.